Question

For each of these lists of integers, find a simple formula or rule that generates the terms of an integer sequence that begins with the given list. assuming that your formula or rule is correct, determine the next three terms of the sequence. 2, 4, 16, . . . multiple choice

a. the next three terms are 64, 256, 1024.
b. the next three terms are 64, 2048, 262144.
c. the next three terms are 256, 4096, 65536.

Answer 1

Answer: The first 3 terms being 2, 4, 16, .... the correct answer for the next 3 terms is option (a) 64, 256, 1024.

Step-by-step explanation: These are sequencing type of problems. In these, based on the given few terms, you are supposed to find the pattern and then use this pattern to identify the term in question.

In the given question, the given terms are 2, 4 and 16. Usually when the consequent numbers jump so fast, example 4 ---> 16, you need to think in terms of squares and cubes (power of the number). So, as you can guess,

Second term is 2 to the power of 2, that is 2 square or 4.

Third term is 2 to the power of 4, that is 16

So, fourth term should be 2 to the power of 6, that is 64.

5th term is 2 to the power of 8, that is 256 and next term is 1024, because it is 2 to the power of 10.

Thus the pattern is that the base value being 2, the power of 2 is jumping by the list of consequent even numbers, i.e 2, 4, 6, 8 and 10.